Solve for $x$ and $y$ using elimination. $\begin{align*}-4x-8y &= 2 \\ 2x+y &= 2\end{align*}$
Answer: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $1$ and the bottom equation by $2$ $\begin{align*}-4x-8y &= 2\\ 4x+2y &= 4\end{align*}$ Add the top and bottom equations. $-6y = 6$ Divide both sides by $-6$ and reduce as necessary. $y = -1$ Substitute $-1$ for $y$ in the top equation. $-4x-8( -1) = 2$ $-4x+8 = 2$ $-4x = -6$ $x = \dfrac{3}{2}$ The solution is $\enspace x = \dfrac{3}{2}, \enspace y = -1$.